This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data in an intermediate maximum (i.e., “hump” shaped) relationship. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.
Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.
Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:
model 1: simple model \(G = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 2: phi model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 3: phi-alpha model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot based filtering criteria:
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1677 observations.
Below the model fitting procedure is implemented by ecoprovince:
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6799 5243.9
## 2 6798 5240.3 1 3.547 4.6014 0.03198 *
## 3 6797 4946.6 1 293.714 403.5836 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25284.27
## 2 2 25281.66
## 3 3 24891.20
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.292872 0.163470 1.792 0.0732 .
## phi 0.010286 0.004348 2.366 0.0180 *
## alpha 0.644419 0.030041 21.451 <2e-16 ***
## a -6.319123 16.323713 -0.387 0.6987
## b 9.731894 16.313339 0.597 0.5508
## c 29.516194 1.963439 15.033 <2e-16 ***
## d 4.920382 4.450084 1.106 0.2689
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8531 on 6797 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 7.621e-06
## (2 observations deleted due to missingness)
## Warning: Removed 1 rows containing missing values (geom_point).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18726 16075
## 2 18721 16009 5 66.26 15.498 3.029e-15 ***
## 3 18720 14917 1 1091.78 1370.124 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 65771.72
## 2 2 65686.39
## 3 3 64365.59
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.885982 0.141057 6.281 3.44e-10 ***
## phi 0.025852 0.002867 9.018 < 2e-16 ***
## alpha 0.827263 0.020518 40.319 < 2e-16 ***
## a 0.722858 0.373130 1.937 0.0527 .
## b 1.832104 0.365116 5.018 5.27e-07 ***
## c 19.734593 0.815916 24.187 < 2e-16 ***
## d 2.337867 0.345363 6.769 1.33e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8927 on 18720 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 2.592e-06
## (48 observations deleted due to missingness)
## Warning: Removed 23 rows containing missing values (geom_point).
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_221$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_221.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Error in nls(fg2_1, data = G_222, start = c(ge = ge.start, a = a.start, :
## singular gradient
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_222$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_222.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8769 9241.0
## 2 8768 9226.3 1 14.662 13.933 0.0001906 ***
## 3 8764 9007.0 4 219.303 53.346 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 35056.50
## 2 2 35044.56
## 3 3 34826.34
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.129281 0.098622 -11.451 < 2e-16 ***
## phi -0.022440 0.005652 -3.970 7.25e-05 ***
## alpha 0.584152 0.038447 15.194 < 2e-16 ***
## a 2.669375 0.482960 5.527 3.35e-08 ***
## b 1.970422 0.471662 4.178 2.97e-05 ***
## c 29.057795 1.872699 15.517 < 2e-16 ***
## d 1.426937 0.289803 4.924 8.64e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.014 on 8764 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 2.379e-06
## (12 observations deleted due to missingness)
## Warning: Removed 5 rows containing missing values (geom_point).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12311 21643
## 2 12310 21640 1 2.8 1.591 0.2072
## 3 12309 19118 1 2522.2 1623.870 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 60187.33
## 2 2 60187.74
## 3 3 58663.54
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.0986057 0.0991469 -0.995 0.320
## phi 0.0007941 0.0040244 0.197 0.844
## alpha 0.8567398 0.0191847 44.658 <2e-16 ***
## a 3.2349735 0.2112777 15.311 <2e-16 ***
## b 3.2164895 0.1944758 16.539 <2e-16 ***
## c 18.2273027 0.4124116 44.197 <2e-16 ***
## d 1.3141944 0.0855111 15.369 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.246 on 12309 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 6.922e-06
## (31 observations deleted due to missingness)
## Warning: Removed 14 rows containing missing values (geom_point).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12395 26336
## 2 12394 26317 1 18.36 8.6448 0.003286 **
## 3 12393 23747 1 2570.16 1341.3010 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 61358.26
## 2 2 61351.61
## 3 3 60079.33
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.006466 0.122537 0.053 0.9579
## phi 0.008872 0.004511 1.967 0.0493 *
## alpha 0.842963 0.020444 41.232 <2e-16 ***
## a 3.481881 0.118222 29.452 <2e-16 ***
## b 2.594932 0.109338 23.733 <2e-16 ***
## c 16.557370 0.402833 41.102 <2e-16 ***
## d 0.923104 0.049522 18.640 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.384 on 12393 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.51e-06
## (70 observations deleted due to missingness)
## Warning: Removed 29 rows containing missing values (geom_point).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1255 2849.6
## 2 1254 2849.5 1 0.12 0.0529 0.8181
## 3 1253 2692.6 1 156.84 72.9850 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6292.826
## 2 2 6294.773
## 3 3 6225.438
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.870346 0.901176 0.966 0.334336
## phi -0.009029 0.021670 -0.417 0.677010
## alpha 0.784819 0.082801 9.478 < 2e-16 ***
## a 3.281058 0.556974 5.891 4.93e-09 ***
## b 1.518118 0.413630 3.670 0.000253 ***
## c 18.156020 2.676847 6.783 1.81e-11 ***
## d 0.782773 0.244040 3.208 0.001373 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.466 on 1253 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 8.926e-06
## (5 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96816, p-value = 5.09e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.1636, p-value = 0.001558
## alternative hypothesis: two.sided
## Warning: Removed 3 rows containing missing values (geom_point).
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in nls(fg2_2, data = G_242, start = c(ge = ge.start, phi = phi.start, :
## singular gradient
## Error in nls(fg2_3, data = G_242, start = c(ge = ge.start, phi = phi.start, :
## singular gradient
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1784 1637.6
## 2 1783 1633.2 1 4.3616 4.7617 0.02923 *
## 3 1782 1617.6 1 15.6039 17.1896 3.542e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6743.615
## 2 2 6740.844
## 3 3 6725.669
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.54768 0.29899 -1.832 0.0671 .
## phi 0.02158 0.01084 1.992 0.0466 *
## alpha 0.40164 0.09302 4.318 1.66e-05 ***
## a -0.12904 5.50243 -0.023 0.9813
## b 3.43455 5.50316 0.624 0.5326
## c 29.00246 6.18140 4.692 2.91e-06 ***
## d 3.46196 3.40815 1.016 0.3099
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9528 on 1782 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 6.493e-06
## (8 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93225, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.924, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 4 rows containing missing values (geom_point).
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Error in nls(fg2_1, data = G_263, start = c(ge = ge.start, a = a.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg2_2, data = G_263, start = c(ge = ge.start, phi = phi.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg2_3, data = G_263, start = c(ge = ge.start, phi = phi.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_315.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Error in nls(fg2_1, data = G_322, start = c(ge = ge.start, a = a.start, :
## missing or negative weights not allowed
## Error in nls(fg2_2, data = G_322, start = c(ge = ge.start, phi = phi.start, :
## missing or negative weights not allowed
## Error in nls(fg2_3, data = G_322, start = c(ge = ge.start, phi = phi.start, :
## missing or negative weights not allowed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6722 4631.1
## 2 6721 4611.3 1 19.79 28.851 8.08e-08 ***
## 3 6720 4290.0 1 321.32 503.331 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24157.98
## 2 2 24131.16
## 3 3 23647.28
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.839969 0.191442 4.388 1.16e-05 ***
## phi 0.017844 0.004027 4.431 9.53e-06 ***
## alpha 0.638474 0.026475 24.116 < 2e-16 ***
## a 2.450566 0.125126 19.585 < 2e-16 ***
## b 0.708020 0.082579 8.574 < 2e-16 ***
## c 27.878887 1.761763 15.824 < 2e-16 ***
## d 0.942137 0.155951 6.041 1.61e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.799 on 6720 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 5.478e-06
## (2 observations deleted due to missingness)
## Warning: Removed 1 rows containing missing values (geom_point).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8028 11387
## 2 8027 11381 1 6.68 4.7111 0.03 *
## 3 8026 11111 1 269.82 194.9038 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 36089.85
## 2 2 36087.14
## 3 3 35896.40
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.408200 0.127552 -3.200 0.00138 **
## phi -0.009929 0.005572 -1.782 0.07478 .
## alpha 0.726136 0.049523 14.663 < 2e-16 ***
## a 3.204776 0.316637 10.121 < 2e-16 ***
## b 1.983587 0.276232 7.181 7.55e-13 ***
## c 26.015032 1.721337 15.113 < 2e-16 ***
## d 1.219745 0.203133 6.005 2.00e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.177 on 8026 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.777e-06
## (1 observation deleted due to missingness)
## Warning: Removed 1 rows containing missing values (geom_point).
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 3510.88
## 2 2 NA
## 3 3 NA
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.4228 1.2810 1.891 0.05892 .
## a 1.5037 0.2854 5.268 1.73e-07 ***
## b 1.0411 0.3042 3.422 0.00065 ***
## c 25.8961 2.6460 9.787 < 2e-16 ***
## d 0.5208 0.1315 3.961 8.08e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.126 on 877 degrees of freedom
##
## Number of iterations to convergence: 18
## Achieved convergence tolerance: 7.76e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.98047, p-value = 1.762e-09
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.1975, p-value = 0.2311
## alternative hypothesis: two.sided
## Error in nls(fg2_1, data = G_M231, start = c(ge = ge.start, a = a.start, :
## number of iterations exceeded maximum of 50
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M231$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M231.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3138 7449.1
## 2 3137 7446.7 1 2.39 1.0065 0.3158
## 3 3132 7043.5 5 403.23 35.8603 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 15644.22
## 2 2 15645.21
## 3 3 15457.14
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.091782 0.342038 -3.192 0.00143 **
## phi -0.004369 0.015974 -0.274 0.78446
## alpha 0.997556 0.068924 14.473 < 2e-16 ***
## a 4.878930 0.466285 10.463 < 2e-16 ***
## b 3.462861 0.526379 6.579 5.54e-11 ***
## c 33.740147 1.345010 25.085 < 2e-16 ***
## d 0.412764 0.049270 8.378 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.5 on 3132 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.439e-06
## (40 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95864, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.648, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 7 rows containing missing values (geom_point).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1939 3672.5
## 2 1938 3467.6 1 204.88 114.5044 < 2.2e-16 ***
## 3 1929 3346.6 9 121.07 7.7541 2.764e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8948.829
## 2 2 8839.235
## 3 3 8742.612
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.52119 0.30445 -4.997 6.36e-07 ***
## phi 0.18344 0.01370 13.394 < 2e-16 ***
## alpha 0.76789 0.08709 8.817 < 2e-16 ***
## a 3.08729 1.55632 1.984 0.04743 *
## b 4.49689 1.54267 2.915 0.00360 **
## c 35.53892 7.53152 4.719 2.54e-06 ***
## d 1.93337 0.66181 2.921 0.00353 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.317 on 1929 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 2.342e-06
## (27 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96034, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.6402, p-value = 0.008286
## alternative hypothesis: two.sided
## Warning: Removed 6 rows containing missing values (geom_point).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2604 2857.0
## 2 2603 2850.5 1 6.585 6.0134 0.01426 *
## 3 2594 2650.2 9 200.295 21.7833 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9021.477
## 2 2 9017.457
## 3 3 8812.761
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.65586 0.47035 -1.394 0.16331
## phi 0.03633 0.01614 2.251 0.02447 *
## alpha 0.84555 0.05293 15.975 < 2e-16 ***
## a 0.68227 0.94027 0.726 0.46814
## b 2.02084 0.96660 2.091 0.03665 *
## c 56.12184 4.44187 12.635 < 2e-16 ***
## d 2.01474 0.67929 2.966 0.00304 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.011 on 2594 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.49e-06
## (48 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88013, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.8595, p-value = 6.912e-12
## alternative hypothesis: two.sided
## Warning: Removed 12 rows containing missing values (geom_point).
## Error in nls(fg2_1, data = G_M333, start = c(ge = ge.start, a = a.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M333$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M333.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in nls(fg2_3, data = G_M334, start = c(ge = ge.start, phi = phi.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M334$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M334.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3 |
| 212 | Laurentian Mixed Forest | 3 |
| 221 | Eastern Broadleaf Forest | NA |
| 222 | Midwest Broadleaf Forest | NA |
| 223 | Central Interior Broadleaf Forest | 3 |
| 231 | Southeastern Mixed Forest | 3 |
| 232 | Outer Coastal Plain Mixed Forest | 3 |
| 234 | Lower Mississippi Riverine Forest | 3 |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 3 |
| 255 | Prairie Parkland (Subtropical) | NA |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | NA |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3 |
| M223 | Ozark Broadleaf Forest Meadow | 1 |
| M231 | Ouachita Mixed Forest | NA |
| M242 | Cascade Mixed Forest | 3 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 3 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA |
| M334 | Black Hills Coniferous Forest | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | alpha | alpha.2.5 | alpha.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6806 | 2847 | 0.2928722 | -0.0275809 | 0.6133253 | 0.0102855 | 0.0017619 | 0.0188092 | 0.6444186 | 0.5855286 | 0.7033086 | -6.3191225 | -38.3187109 | 25.680466 | 9.7318944 | -22.2473568 | 41.7111455 | 29.51619 | 25.66724 | 33.36515 | 4.9203821 | -3.8031757 | 13.6439400 |
| 212 | Laurentian Mixed Forest | east | 18775 | 8891 | 0.8859822 | 0.6094972 | 1.1624673 | 0.0258523 | 0.0202335 | 0.0314711 | 0.8272635 | 0.7870466 | 0.8674804 | 0.7228585 | -0.0085100 | 1.454227 | 1.8321037 | 1.1164438 | 2.5477637 | 19.73459 | 18.13532 | 21.33386 | 2.3378675 | 1.6609244 | 3.0148105 |
| 221 | Eastern Broadleaf Forest | east | 7170 | 3490 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 222 | Midwest Broadleaf Forest | east | 4877 | 2401 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 223 | Central Interior Broadleaf Forest | east | 8783 | 3725 | -1.1292810 | -1.3226030 | -0.9359591 | -0.0224402 | -0.0335203 | -0.0113600 | 0.5841517 | 0.5087863 | 0.6595171 | 2.6693754 | 1.7226598 | 3.616091 | 1.9704217 | 1.0458534 | 2.8949900 | 29.05780 | 25.38686 | 32.72873 | 1.4269371 | 0.8588555 | 1.9950187 |
| 231 | Southeastern Mixed Forest | east | 12347 | 5691 | -0.0986057 | -0.2929491 | 0.0957377 | 0.0007941 | -0.0070943 | 0.0086826 | 0.8567398 | 0.8191348 | 0.8943448 | 3.2349735 | 2.8208361 | 3.649111 | 3.2164895 | 2.8352865 | 3.5976925 | 18.22730 | 17.41891 | 19.03569 | 1.3141944 | 1.1465794 | 1.4818095 |
| 232 | Outer Coastal Plain Mixed Forest | east | 12470 | 6101 | 0.0064662 | -0.2337262 | 0.2466585 | 0.0088722 | 0.0000291 | 0.0177152 | 0.8429634 | 0.8028894 | 0.8830374 | 3.4818813 | 3.2501488 | 3.713614 | 2.5949315 | 2.3806130 | 2.8092501 | 16.55737 | 15.76776 | 17.34698 | 0.9231039 | 0.8260340 | 1.0201738 |
| 234 | Lower Mississippi Riverine Forest | east | 1265 | 714 | 0.8703464 | -0.8976346 | 2.6383273 | -0.0090288 | -0.0515430 | 0.0334854 | 0.7848195 | 0.6223761 | 0.9472628 | 3.2810584 | 2.1883541 | 4.373763 | 1.5181181 | 0.7066343 | 2.3296020 | 18.15602 | 12.90442 | 23.40762 | 0.7827729 | 0.3040002 | 1.2615457 |
| 242 | Pacific Lowland Mixed Forest | pacific | 81 | 81 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1797 | 809 | -0.5476846 | -1.1340860 | 0.0387169 | 0.0215844 | 0.0003274 | 0.0428414 | 0.4016421 | 0.2191965 | 0.5840877 | -0.1290406 | -10.9209373 | 10.662856 | 3.4345485 | -7.3587801 | 14.2278772 | 29.00246 | 16.87890 | 41.12601 | 3.4619597 | -3.2224364 | 10.1463557 |
| 255 | Prairie Parkland (Subtropical) | pacific | 663 | 293 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 24 | 24 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 155 | 155 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 215 | 215 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 304 | 240 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 195 | 106 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | interior west | 62 | 62 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 121 | 120 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 93 | 61 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6729 | 2989 | 0.8399694 | 0.4646825 | 1.2152563 | 0.0178435 | 0.0099492 | 0.0257379 | 0.6384745 | 0.5865748 | 0.6903741 | 2.4505658 | 2.2052783 | 2.695853 | 0.7080204 | 0.5461401 | 0.8699006 | 27.87889 | 24.42527 | 31.33250 | 0.9421365 | 0.6364232 | 1.2478498 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8034 | 3700 | -0.4082001 | -0.6582347 | -0.1581655 | -0.0099293 | -0.0208518 | 0.0009931 | 0.7261363 | 0.6290585 | 0.8232142 | 3.2047759 | 2.5840854 | 3.825466 | 1.9835873 | 1.4421005 | 2.5250742 | 26.01503 | 22.64076 | 29.38930 | 1.2197454 | 0.8215529 | 1.6179378 |
| M223 | Ozark Broadleaf Forest Meadow | east | 883 | 343 | 2.4227544 | -0.0915226 | 4.9370314 | NA | NA | NA | NA | NA | NA | 1.5037012 | 0.9435126 | 2.063890 | 1.0411436 | 0.4440579 | 1.6382293 | 25.89607 | 20.70279 | 31.08934 | 0.5208208 | 0.2627350 | 0.7789067 |
| M231 | Ouachita Mixed Forest | east | 988 | 481 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | pacific | 3179 | 3176 | -1.0917823 | -1.7624233 | -0.4211414 | -0.0043693 | -0.0356894 | 0.0269508 | 0.9975558 | 0.8624148 | 1.1326968 | 4.8789296 | 3.9646741 | 5.793185 | 3.4628610 | 2.4307789 | 4.4949430 | 33.74015 | 31.10296 | 36.37734 | 0.4127636 | 0.3161582 | 0.5093689 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1963 | 1963 | -1.5211913 | -2.1182783 | -0.9241044 | 0.1834450 | 0.1565842 | 0.2103058 | 0.7678897 | 0.5970888 | 0.9386907 | 3.0872948 | 0.0350396 | 6.139550 | 4.4968882 | 1.4714163 | 7.5223600 | 35.53892 | 20.76815 | 50.30968 | 1.9333652 | 0.6354259 | 3.2313045 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 19 | 19 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 362 | 362 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1711 | 1711 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2649 | 2648 | -0.6558624 | -1.5781636 | 0.2664388 | 0.0363264 | 0.0046821 | 0.0679706 | 0.8455463 | 0.7417608 | 0.9493318 | 0.6822728 | -1.1614916 | 2.526037 | 2.0208352 | 0.1254576 | 3.9162128 | 56.12184 | 47.41187 | 64.83181 | 2.0147404 | 0.6827438 | 3.3467371 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1675 | 1675 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | interior west | 362 | 170 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 213 | 213 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning: Removed 23 rows containing missing values (geom_point).
## Warning: Removed 23 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_hline).
## Warning: Removed 23 rows containing missing values (geom_point).
## Warning: Removed 23 rows containing missing values (geom_point).
## region weighted.ge
## 1 entire US -0.03960663
## 2 pacific -1.13380170
## 3 east 0.14185716
## 4 interior west -0.22981654
## region weighted.phi
## 1 entire US 0.012690540
## 2 pacific 0.060826694
## 3 east 0.006197611
## 4 interior west 0.012728892
## region weighted.alpha
## 1 entire US 0.6087266
## 2 pacific 0.8214344
## 3 east 0.6359597
## 4 interior west 0.2962825
## region weighted.ge
## 1 entire US -0.0462044
## 2 pacific -1.2558084
## 3 east 0.1506365
## 4 interior west -0.6558624
## region weighted.phi
## 1 entire US 0.014804563
## 2 pacific 0.067372162
## 3 east 0.006581174
## 4 interior west 0.036326372
## region weighted.alpha
## 1 entire US 0.7101298
## 2 pacific 0.9098277
## 3 east 0.6753185
## 4 interior west 0.8455463